Research ArticleCONDENSED MATTER PHYSICS

Realization of an intrinsic ferromagnetic topological state in MnBi8Te13

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Science Advances  22 Jul 2020:
Vol. 6, no. 30, eaba4275
DOI: 10.1126/sciadv.aba4275

Abstract

Novel magnetic topological materials pave the way for studying the interplay between band topology and magnetism. However, an intrinsically ferromagnetic topological material with only topological bands at the charge neutrality energy has so far remained elusive. Using rational design, we synthesized MnBi8Te13, a natural heterostructure with [MnBi2Te4] and [Bi2Te3] layers. Thermodynamic, transport, and neutron diffraction measurements show that despite the adjacent [MnBi2Te4] being 44.1 Å apart, MnBi8Te13 manifests long-range ferromagnetism below 10.5 K with strong coupling between magnetism and charge carriers. First-principles calculations and angle-resolved photoemission spectroscopy measurements reveal it is an axion insulator with sizable surface hybridization gaps. Our calculations further demonstrate the hybridization gap persists in the two-dimensional limit with a nontrivial Chern number. Therefore, as an intrinsic ferromagnetic axion insulator with clean low-energy band structures, MnBi8Te13 serves as an ideal system to investigate rich emergent phenomena, including the quantized anomalous Hall effect and quantized magnetoelectric effect.

INTRODUCTION

Over the past decade, topology has taken the center stage in condensed matter physics and materials science, emerging as an organizing principle of the states of matter (1). Many topological phases, such as quantum spin Hall insulators, quantum anomalous Hall (QAH) insulators, three-dimensional (3D) topological insulators (TIs), and Weyl semimetals, have been observed (2, 3). Despite tremendous progress, the dominant majority of known topological materials (apart from the QAH insulators) are nonmagnetic materials, whereas studies on magnetic topological materials have been far more limited. In contrast to their nonmagnetic counterparts, magnetic topological materials allow a distinct set of new topological states including the axion insulator, the magnetic Weyl semimetals, the Chern insulators, and the 3D QAH insulators (2, 3). Furthermore, magnetism is a natural way to induce nonnegligible electronic interactions, paving the way for studying the interplay between band topology and correlations. Therefore, topological magnetic materials have emerged as the frontier of the field. Since the realization of the QAH state in the magnetically doped TI thin films Cr0.15(Bi0.1Sb0.9)1.85Te3 (4), recent studies have identified a range of topological magnetic materials such as Fe3Sn2, Co3Sn2S2, Mn3Ge, and Co2MnGa (59). However, the magnetically doped TI thin films are nonstoichiometric systems where disorder and inhomogeneity are unavoidable. Fe3Sn2, Co3Sn2S2, Mn3Ge, and Co2MnGa are all large carrier density metals where substantial topologically trivial bands coexist with the topological bands at the chemical potential (59). To avoid these drawbacks, an intrinsically ferromagnetic (FM) topological material with magnetic ions occupying their own crystallographic sites and with only the topological bands at the charge neutrality energy is strongly desired but has so far remained elusive.

Recently, MnBi2Te4, a van der Waals (vdW) compound composed of the septuple layers (SLs) of [MnBi2Te4], was identified as an intrinsic magnetic topological material with clean band structure (1032). Unfortunately, magnetic moments in MnBi2Te4 are antiferromagnetically (AFM) coupled across adjacent [MnBi2Te4] planes (15, 31). Therefore, although the quantized anomalous Hall conductance was observed at a record-breaking temperature of 4.5 K, it requires an external magnetic field as large as 12 T to polarize the system into the FM state (21, 22). Can we reduce the interlayer AFM coupling between the adjacent Mn layers to realize intrinsic FM? One material design strategy is to increase the interlayer distance between the adjacent Mn layers. How can we achieve it? Structurally, SL blocks have great compatibility with quintuple (QL) blocks of [Bi2Te3], as suggested by the existence of GeBi4Te7, which has alternating [GeBi2Te4] SL and [Bi2Te3] QL building blocks (33). This superior compatibility provides us flexible structural control to reduce the interlayer magnetic coupling by increasing the interlayer distance between the adjacent [MnBi2Te4] layers. Based on our material design strategy, here, we report the discovery of an intrinsic FM TI MnBi8Te13. Despite the interlayer distance between the adjacent [MnBi2Te4] SLs being 44.1 Å, it is striking and surprising that our thermodynamic, transport, and neutron diffraction measurements indicate that MnBi8Te13 has long-range FM order below 10.5 K, with the easy axis along the c axis. Our first-principles calculations and angle-resolved photoemission spectroscopy (ARPES) measurements further suggest that it is an intrinsic FM axion state. Considering the natural heterostructure nature of MnBi8Te13, our finding provides a superior material realization to explore zero-field QAH effect, quantized topological magnetoelectric effect, and associated phenomena.

RESULTS

Crystal structure of MnBi8Te13

Although the existence of MnBi8Te13 was mentioned (34), its crystal structure was never reported, partially due to the difficulty in growing the MnBi8Te13 phase and separating it from the other members in the MnBi2nTe3n+1 family. We managed to grow high-quality MnBi8Te13 single crystals and solved the crystal structure of MnBi8Te13 by refining the room-temperature powder x-ray diffraction (XRD) pattern using various structure models. We found that MnBi8Te13 crystallizes in the R-3m space group with the lattice parameters: a = b = 4.37485(7) Å, c = 132.415(3) Å, α = β = 90°, γ = 120°. The refinement results and structural parameters are summarized in tables S1 and S2. The powder XRD pattern and the Rietveld refinement are shown in Fig. 1A. The low-angle diffraction peaks can be well indexed as the (0 0 L) with lattice parameter c as 132.415(3) Å (see the inset of Fig. 1A), which is longer than the parameter c of 101.825(8) Å in MnBi6Te10. The formation of MnBi8Te13 is also visualized by the scanning transmission electron microscopy (STEM) image, as shown in Fig. 1B. The STEM image shows vdW structures, which is composed of repeating units of one SL block made of seven atomic layers and three consecutive QL blocks made of five atomic layers. The chemical analysis via the wavelength dispersive spectroscopy measurement results in the elemental composition of the sample as Mn:Bi:Te = 0.74(3):8.2(1):13, where the Mn:Bi ratio is slightly smaller than the ideal 1:8. The smaller than ideal Mn:Bi ratio is also observed in other MnBi2nTe3n+1 because of the Bi substitution on Mn sites (16, 31).

Fig. 1 Crystal structure of MnBi8Te13.

(A) Powder XRD and the refinement of MnBi8Te13. Inset: Low-angle (0 0 l) XRD peaks of the cleaved ab surface of MnBi8Te13. a.u., arbitrary units. (B) STEM images of MnBi8Te13 made on a focused-ion beam sample. The purple blocks label the [MnBi2Te4] SL, and the blue blocks mark the [Bi2Te3] QL. (C) Schematic drawing of the crystal and magnetic structure of MnBi2nTe3n+1 (n = 0, 1, 2, 3, and 4) with the stacking sequence listed. A, B, and C represent the bilayers of BiTe6 octahedra whose bottom Te atoms, center Bi atoms, and top Te atoms are on the cell edges, respectively. Magenta arrow, magnetic structure in the order state; blue block, edge-sharing BiTe6 octahedra; magenta block, edge-sharing MnTe6 octahedra, which are connected to the blue block via edge sharing. Inset: Tc (the critical temperatures) versus dMn-Mn (the interlayer distance between the adjacent Mn-Mn layers) and n versus dMn-Mn in MnBi2nTe3n+1 (n = 1, 2, 3, and 4).

The crystal structure is shown in Fig. 1C. It is characterized by the alternating stacking of monolayer of MnTe6 octahedra that are well separated by a number of monolayers of BiTe6 octahedra running along the c axis. The distance between the nearest Mn-Mn interlayers is 44.1 Å, which is much larger than 13.6 Å for MnBi2Te4, 23.8 Å for MnBi4Te7, and 33.9 Å for MnBi6Te10, as shown in the inset of Fig. 1C. The stacking sequence of the MnBi2nTe3n+1 series can be rationalized (31). Using Bi2Te3 shown in Fig. 1C as the starting point, along the c axis, the stacking sequence of Bi2Te3 is -A-B-C-A-B-C-, where A, B, and C represent the bilayers of BiTe6 octahedra whose bottom Te atoms, center Bi atoms, and top Te atoms are on the cell edges, respectively. The “Mn” layer can replace “A” or “B” or “C” bilayers of BiTe6 octahedra to make MnBi2nTe3n+1. For example, as shown in Fig. 1C, for MnBi2Te4, the stacking sequence is -Mn(B)-C-Mn(A)-B-Mn(C)-A-; for MnBi4Te7, the stacking sequence is -Mn(B)-C-A-; and for MnBi6Te10, the stacking sequence is -Mn(B)-C-A-B-Mn(C)-A-B-C-Mn(A)-B-C-A-. When it comes to MnBi8Te13, the stacking sequence is Mn(B)-C-A-B-C-Mn(A)-B-C-A-B-Mn(C)-A-B-C-A-, exactly identical to the one we obtained based on our powder x-ray refinement. Therefore, with the stacking rule, we can easily assign the stacking sequence for the yet-to-be-discovered higher n members of MnBi2nTe3n+1 or design new magnetic TIs with the QL and SL building blocks.

Long-range ferromagnetism and its strong coupling with charge carriers in MnBi8Te13

As a comparison, the physical properties of MnBi6Te10 where two [Bi2Te3] QLs are sandwiched between the adjacent [MnBi2Te4] SLs are also presented. The inset of Fig. 2 (A and B) presents the temperature-dependent specific heat data of MnBi8Te13 and MnBi6Te10, respectively. A specific heat anomaly associated with the magnetic phase transition is observed, which determines the ordering temperature as 10.5 K for MnBi8Te13 and 11.0 K for MnBi6Te10. The magnetic properties of MnBi8Te13 are shown in Fig. 2 (A, C, and E), whereas those of MnBi6Te10 are presented in Fig. 2 (B, D, and F). The data indicate that, with the c axis as the easy axis, MnBi8Te13 is FM below 10.5 K, while MnBi6Te10 is AFM below 11.0 K. Figure 2 (A and B) presents the zero-field-cooled (ZFC) and FC magnetic susceptibility data, χc (Hc) and χab (Hab), measured at 0.1 kOe for MnBi8Te13 and MnBi6Te10, respectively. Sharp contrast can be seen. A large bifurcation of ZFC and FC data of χc appears below 10.5 K in MnBi8Te13, where upon cooling the ZFC data decrease but the FC data increase, suggesting the formation of FM domains. However, for MnBi6Te10, we observed a sharp cusp feature centering at 11.0 K in χc, similar to the ones in AFM MnBi2Te4 and MnBi4Te7 (17, 35) but with a small bifurcation of ZFC and FC data below 9 K. Furthermore, at 2 K, the magnitude of the FC χc in MnBi8Te13 is orders larger than that in AFM MnBi2Te4, MnBi4Te7, and MnBi6Te10 (17, 35). This strongly suggests different types of ground states in these two materials, with MnBi8Te13 being FM and MnBi6Te10 being AFM. Our conclusion is further confirmed by the hysteresis loop of isothermal magnetization curves Mc(H) (Hc) shown in Fig. 2 (C and D) for MnBi8Te13 and MnBi6Te10, respectively. At 2 K, unlike the Mc(H) data where multiple-step features are observed because of the spin-flop transition in MnBi2Te4 (15, 17) and spin-flip transition in MnBi4Te7 (35) and MnBi6Te10, Mc(H) in MnBi8Te13 shows a typical hysteresis loop for FM materials with coercivity of Hc = 0.75 kOe and saturation remanence of Mr = 3.1 μB/Mn. Upon warming, Hc decreases as the hysteresis loop shrinks in area due to the enhanced thermal fluctuations. Figure 2E shows the Mab(H) and Mc(H) of MnBi8Te13 up to 7 T, where a field of 10.4 kOe is required to force spins to saturate in the ab plane. This value is 11.3 kOe for MnBi6Te10 (Fig. 2F). Both sets of data indicate Ising anisotropy, with the c axis as the easy axis in these two compounds. Ising anisotropy has also been suggested in MnBi2Te4 by the inelastic neutron scattering measurement (28). The saturation moment measured at 7 T for MnBi8Te13 is Ms = 3.5(1) μB/Mn, whereas it is 3.4(1) μB/Mn for MnBi6Te10. In both cases, Ms is smaller than 4.6 μB/Mn, the obtained value from our density functional theory (DFT) calculation, but similar to 3.6 μB/Mn in MnBi2Te4 (17) and 3.5 μB/Mn in MnBi4Te7 (35). The reduced Mn saturation moment in MnBi8Te13 is likely due to the Mn site disorder as suggested in MnBi2Te4 and MnBi4Te7 (16,34). The fitted Weiss temperatures of MnBi8Te13 are Θwab = 12.8 K and Θwc = 12.1 K, suggesting FM exchange interactions. The fitted effective moments are μeffab=5.4 μB/Mn and μeffc=5.1 μB/Mn, indicating weak single-ion anisotropy. Although the effective moment is smaller than 5.9 μB/Mn for a Mn2+ ion, it is similar to MnBi2Te4, MnBi4Te7, and MnBi6Te10 (17, 35).

Fig. 2 Transport and thermodynamic properties of MnBi8Te13.

As a comparison, physical properties of MnBi6Te10 are also shown. (A and B) Temperature-dependent susceptibility taken at H = 0.1 kOe for MnBi8Te13 (A) and MnBi6Te10 (B). Inset: Temperature-dependent specific heat: (A) MnBi8Te13 and (B) MnBi6Te10. The criterion to determine Tc and TN is shown in the inset. (C and D) Magnetic hysteresis loop of isothermal magnetization at low fields with Hc for MnBi8Te13 (C) and MnBi6Te10 (D). (E and F) Magnetic hysteresis loop of isothermal magnetization up to 7 T with Hc and Hab: MnBi8Te13 (E) and MnBi6Te10 (F). (G and H) Anisotropic resistivity, ρxx and ρzz, for MnBi8Te13 (G) and MnBi6Te10 (H).

Figure 2G presents the temperature-dependent in-plane (ρxx) and out-of-plane resistivity (ρzz) of MnBi8Te13. Above 20 K, upon cooling, both ρxx and ρzz decrease semilinearly. Upon further cooling, when approaching Tc, because of the stronger scattering from enhanced spin fluctuations, both values increase (36, 37). Then, a sharp drop appears in both curves below 10.5 K due to the loss of spin scattering. The drop in ρzz below Tc is distinct from that in MnBi2Te4, MnBi4Te7, and MnBi6Te10 (see Fig. 2H) (17, 35), where the antiparallelly aligned Mn moments enhance resistivity via the spin-flip scattering. Therefore, the drop in ρzz again suggests FM ordering in MnBi8Te13 because the parallelly aligned Mn moments along the c axis eliminate such spin-flip scattering and thus reduce electric resistivity.

To confirm the long-range FM phase transition in MnBi8Te13, we have performed single-crystal neutron diffraction experiments at various temperatures. The quality of the instrument resolution limited magnetic Bragg peaks indicates that the stacking faults in this crystal are minimal. Figure 3A shows the Bragg reflection (1 0 1) at 4.5 and 15 K. It is evident that the peak intensity enhances substantially from 15 to 4.5 K, indicating the development of long-range magnetic ordering with the propagation vector k = 0. Starting from the nuclear space group R-3m with Mn atoms occupying the Wyckoff position (0, 0, 0) and k = 0, through symmetry analysis (38), we obtained the k-maximal magnetic subgroup as R-3m′ whose symmetry only allows the presence of an FM arrangement with the Mn spins along the c axis. Its magnetic structure is illustrated in Fig. 1C. The order parameter of MnBi8Te13 was measured from 4.5 to 15 K. As shown in Fig. 3B, a power law was used to fit the intensity of magnetic reflection (1 0 1) as a function of temperature. The fit yields the critical temperature 9.8(3) K and a critical exponent β = 0.4(1). The former is consistent with our thermodynamic measurements. The latter is considerably larger than the value of 0.125 expected for the Ising model in two dimensions, excluding this possibility (39). More data at lower temperatures could better define the critical behavior.

Fig. 3 Neutron diffraction data of MnBi8Te13.

(A) Rocking curve scan for Bragg peak (1 0 1) of MnBi8Te13 at 4.5 and 15 K through neutron diffraction. r.l.u., reciprocal lattice units. (B) Temperature-dependent intensity of the magnetic reflection (1 0 1) of MnBi8Te13. The solid line stands for the power-law fit using I=A(1TTc)2β+B, where β is the order parameter critical exponent (39).

Strong coupling between charge carriers and magnetism is observed in MnBi8Te13 through the magnetotransport measurements, as shown in Fig. 4. ρxx(H), ρzz(H), and ρxy(H) follow the same hysteresis as that in M(H). Using n = H/eρxy, our 50-K data correspond to an electron carrier density of 1.66 × 1020 cm−3, similar to that of MnBi2Te4 (26). Figure 4F shows the ρxx(H) curves up to 9 T at various temperatures. The overall “W” shape was observed at low temperatures. The W-shaped MR(H) was previously observed in MnBi4Te738, where it was suggested to be a combination of nonmagnetic parabolic MR contribution and negative MR originating from FM fluctuations. Unlike MnBi4Te7 where the W-shaped behavior was observed far above its transition temperature 13 K, in MnBi8Te13, the MR quickly changes from the deepest W shape at Tc into a parabolic shape at just a few degrees above it. This may suggest weak FM fluctuations above Tc in MnBi8Te13.

Fig. 4 Magnetotransport properties of MnBi8Te13.

(A to C) Field-dependent magnetization M (A), transverse magnetoresistivity of ρxx (B), and Hall resistivity ρxy (C) at 2 K with Iab and Hc. (D and E) Field-dependent magnetization M (D) and transverse magnetoresistivity of ρzz (E) at 2 K with Ic and Hab. (F) Transverse magnetoresistivity of ρxx with Iab and Hc at various temperatures.

FM axion state revealed by DFT calculation

To investigate the band topology, in the FM configuration with the spin oriented along the c axis, we calculated the electronic band structure of MnBi8Te13. Using the experimentally determined lattice parameters and atomic positions, our calculation shows only a continuous bulk energy gap (note S3). In contrast, using the experimental lattice parameters with relaxed atomic positions, our calculation indicates a 170-meV global energy bandgap (Fig. 5B). By comparing our DFT calculation with the experimental ARPES data, the one with relaxed atomic positions describes the material well.

Fig. 5 DFT band structure of MnBi8Te13 calculated using the experimental lattice parameters with relaxed atomic positions.

(A to D) Bulk band structure. Bulk Brillouin zone (BZ) and the (001) surface BZ of MnBi8Te13 with the high symmetry points marked (A). Bulk band structure of MnBi8Te13 in the out-of-plane FM configuration, with spin-orbit coupling and correlation parameter U included (B). Spin-resolved band structure zoom in around the Γ point (C). Orbital-resolved band structure zoom in around the Γ point (D). The red and blue dots indicate Te pz and Bi pz orbitals, respectively. There are clear band inversions between the Te pz and Bi pz states at the Γ point. (E and F) DFT calculation of a seven-layered finite-sized slab model corresponding to the QL1 surface arrangement, i.e., with vacuum-[QL-SL-QL-QL-QL-SL-QL]-vacuum. (E) Band structure of this slab model. The sizes of the blue and red dots represent the fraction of electronic charge residing in the topmost QL and the nearest-neighboring SL, respectively. (F) Evolution of the sum of Wannier charge centers (WCCs) along ky in the kz = 0 plane. The trajectory of WCC is an open curve traversing the whole BZ once, indicating the Chern number C = 1 in the kz = 0 plane.

To highlight the spin splitting in the presence of FM ordering, we present the <Sz> resolved band structure in Fig. 5C. The band structure projected on the Bi p and Te p orbitals shows that the bands near the Fermi level mostly originate from the Bi p and Te p orbitals. As shown in Fig. 5D, there are clear band inversions between the Bi pz and Te pz states. The Bi pz orbitals reach deep into the valence bands, indicating multiple possible band inversions that originate from the different [Bi2Te3] QL and [MnBi2Te4] SL of MnBi8Te13.

The presence of clear band inversions around the Γ point hints toward a topological phase. To unravel the exact topology of this system, we first compute the Chern number in the kz = 0 and kz = π planes. In both planes, the Chern number is found to be zero. Next, we compute the parity-based higher-order Z4 invariant, which is given byZ4=i=18n=1nocc1+ξn(Γi)2mod4(1)

Here, ξni) is the parity of the nth band at the ith time reversal invariant momentum (TRIM) point Γi and nocc is the number of occupied bands. The Z4 invariant is well defined for an inversion symmetric system, even in the absence of time reversal symmetry (4042). The odd values of Z4 (1, 3) indicate a Weyl semimetal phase, while Z4 = 2 implies an insulator phase with a quantized topological magnetoelectric effect (axion coupling θ = π) (43). A detailed list of the number of occupied bands with even (n+occ) and odd (nocc) parity eigenvalues at the eight TRIM points is shown in table S3. Based on this, the computed Z4 invariant is found to be 2, which demonstrates that MnBi8Te13 is an intrinsic FM axion insulator.

It is noted that, in calculations with or without atomic relaxation, the characteristics of band inversion and the topology of whole system remain the same, i.e., an FM axion state. In addition, we have investigated the evolution of the band structures by changing lattice constants a, b (in-plane), and c (out-of-plane) simultaneously. Within the range from −3 to +3% in MnBi8Te13, we did not find any crossing point or the additional band inversion feature. Our calculation reveals that the axion phase in MnBi8Te13 is quite stable.

Surface state revealed by ARPES and DFT

To investigate whether surface states appear in MnBi8Te13, we have performed small-spot (20 μm× 50 μm) ARPES scanned across the surfaces of MnBi8Te13. According to the crystal structure of MnBi8Te13, four different terminations are expected during the cleave, as visualized in the cartoon pictures in Fig. 6. Our ARPES data and DFT calculations reveal distinguishing surface states for the four different terminations of MnBi8Te13, which are summarized in Fig. 6.

Fig. 6 The comparison of ARPES data and DFT calculation on MnBi8Te13.

(A to D) Experimental ARPES isoenergy surfaces at the Fermi level measured with 26 eV, 20 μm×50 μm spot-sized linear horizontal light at 12 K: (A) SL, (B) QL1, (C) QL2, and (D) QL3 termination. All Fermi surfaces show the expected sixfold symmetry with clear distinctions. (E to H) Experimental ARPES E-k spectrum cut along the M → Γ → M high symmetry direction for various terminations. A large and clean gap in the surface states of the QL1 termination is observed in (F), as highlighted by the arrow that points to the charge neutrality point suggested by DFT calculations. (I to L) Calculated DFT E-k spectrum cut along the M → Γ → M high symmetry direction for various terminations. We shift the Fermi level to match the experimentally observed Fermi level for each termination.

Figure 6 (A to D) shows the isoenergy surfaces at the Fermi level, which uniquely fingerprints each of the four possible terminations of MnBi8Te13. We identify a unique circular Fermi surface for the SL termination, which has been observed in other MnBi2nTe3n+1 (n = 1, 2, 3) (4446). We find that the QLn terminations show a dominant sixfold symmetric Fermi surface with decreasing cross-sectional area from QL1 to QL3. Our assignment of the isoenergy surfaces to the respective terminations for MnBi8Te13 is consistent with previous measurements on the simpler MnBi2Te4, MnBi4Te7, and MnBi6Te10 compounds (24, 4446). Figure 6 (E to H) presents the experimental ARPES E-k maps along the M → Γ → M high symmetry direction. Different types of surface states are observed for each of the four terminations. For the SL termination, a gapless or nearly gapless surface state appears (Fig. 6E), consistent with the gapless surface state observed on the SL termination in previous ARPES measurements of MnBi2Te4, MnBi4Te7, and MnBi6Te1 (24, 4446). The QL3 termination, which is unique to MnBi8Te13, shows mass renormalization near the Fermi level (Fig. 6H). Furthermore, a large surface gap of ~105 meV centering around the charge neutrality point of −0.35 eV is revealed in the QL1 termination and is highlighted by the arrow (Fig. 6F). We find that the spectra taken below and above the transition temperature are very similar in terms of the size of the gap, except for thermal broadening of the electrons (note S2). This has been observed in various magnetic TIs, including MnBi2Te4, MnBi4Te7, and MnBi6Te10, and the origin of it is under debate (24, 47). This aspect will also be discussed more in note S2.

To confirm the topological nature of MnBi8Te13, we calculated the surface spectral weight throughout the (001) surface Brillouin zone (BZ) using the semi-infinite Green’s function approach for SL, QL1, QL2, and QL3 terminations correspondingly, as shown in Fig. 6 (I to L). Each state is plotted with a color corresponding to the integrated charge density of the state within the topmost QL or SL. In addition, we shift the Fermi level to match the experimentally observed Fermi level.

Excellent agreement between the experimental ARPES data and DFT calculation is achieved for the QLn terminations as shown in Fig. 6. Our calculation suggests that the sizable surface bandgap presented in the QL1 termination around −0.35 eV is a hybridization gap induced from the hybridization effect between the topmost QL and the nearest-neighboring SL (note S4). Although the calculated bandgap value is smaller than that from ARPES, it is a well-known problem in that generalized gradient approximation (GGA) generally underestimates the bandgap in semiconductors and insulators (48, 49). The hybridization gap seems universal in MnBi2nTe3n+1, which has been suggested for MnBi6Te10 (50) and MnBi4Te7 (51). However, until now, it is unclear if the hybridization gap exists and supports QAH in the 2D limit. To settle down this issue, we have performed DFT calculation on a seven-layered finite-sized slab model with the arrangement of vacuum-[QL-SL-QL-QL-QL-SL-QL]-vacuum, i.e., a structure that has the QL1 termination on both surfaces. The main features of the slab results shown in Fig. 5E are consistent with our semi-infinite Green’s function approach. We then calculate the Chern number of this slab model based on the Wilson loop method (52). Our result shows a nontrivial Chern number (C = 1) in this hybridization gap (Fig. 5F), demonstrating that MnBi8Te13 is a QAH insulator in its 2D limit if the Fermi level is gated to the middle of the large hybridization gap.

As a consequence of strong exchange fields from the Mn magnetic layer in the SL termination, our calculation on the SL termination results in a parabolic large gapped surface band dispersion in the bulk energy gap (Fig. 6I). This is in sharp contrast with the gapless Dirac surface state revealed by the ARPES (Fig. 6E). For the SL termination, the deviation between ARPES and DFT calculation as well as the gapless Dirac surface state are universal in the MnBi2nTe3n+1 family (n = 1, 2, 3) (24, 4446). The unexpected gapless surface state is argued to be caused by the surface spin reconstruction when the magnetic [MnBi2Te4] layer is at the vacuum-sample interface (24, 45, 46). Further experiments in identifying the spin reconstruction on the SL termination are urged to settle down this issue.

DISCUSSION

We have presented the realization of the intrinsic FM topological material, MnBi8Te13. Our work has several implications. First, our theoretical calculations show that MnBi8Te13 is an FM axion insulator. Such a topological axion state suggests a quantized magnetoelectric coupling and an emergent axion electrodynamics. Therefore, the optical responses of MnBi8Te13, especially in the terahertz regime, may be of great interest. Second, the intrinsic ferromagnetism paves the way for the realization of QAH state at zero magnetic field. Third, when it is exfoliated into the 2D version, the superlattice nature and the stacking of vdW MnBi8Te13 make it possible to fabricate richer combinations of natural heterostructures than those from AFM MnBi2nTe3n+1 (n = 1, 2, 3). Various emergent properties such as QAH state and Quantum Spin Hall state are proposed (36) for such heterostructures. Furthermore, the observation of long-range magnetic order is notable considering the extremely large separation of 44.1 Å between the adjacent [MnBi2Te4] SLs; further investigations will shed light on the mechanism of the long-range magnetic ordering in MnBi8Te13 and will advance our understanding on the magnetism in vdW materials. Last, our work here generally establishes natural heterostructuring as a powerful way to rationally design and control magnetism and other broken symmetry states in layered vdW materials.

METHODS

Sample growth and characterization

We grew single crystals of MnBi2nTe3n+1 (n = 3 and 4) using self-flux (17, 35). Around 20 g of Mn, Bi, and Te elements with the molar ratio of MnTe:Bi2Te3 as 15:85 was loaded into a 5-ml alumina crucible and then sealed inside a quartz tube under one-third atmosphere of Ar. The sample ampule was heated up to 900°C, stayed for 5 hours, and then quickly air-quenched to room temperature. It was then placed inside a furnace, which was preheated to 595°C. The ampule stayed at 595°C for 5 hours and then slowly cooled down to the decanting temperature in 48 hours. We then let the ampule stay at the decanting temperature for about 24 hours before we separated the single crystals from the liquid flux using a centrifuge. By varying the decanting temperature, we could obtain different phases of MnBi2nTe3n+1 (note S1). We found out that the growth window for MnBi4Te7 and MnBi6Te10 is around 2°, while the one for MnBi8Te13 is limited to be only 1° barely above the melting temperature of the flux. The method to determine the decanting temperature for each phase is described in note S1 in detail. Bi2Te3 is the inevitable side product. We also noticed that with increasing n numbers, the chance of the intergrowth between Bi2Te3 and MnBi2nTe3n+1 (n = 3, 4) got enhanced. Therefore, extra care was paid in screening out the right piece. XRD at low angles for both the top and bottom (0 0 l) surfaces as well as powder XRD were performed on a PANalytical Empyrean diffractometer (Cu Ka radiation). Structural determination based on powder XRD was done using FullProf Suite software (53). STEM was measured on a sample prepared by focused-ion beam, and images are made on a Cs-corrected transmission electron microscope (Titan, Thermo Fisher Scientific, FEI) at 300 kV. Images are Bragg-filtered. Electric resistivity was measured in a Quantum Design (QD) DynaCool Physical Properties Measurement System. All samples were shaped into thin rectangular bars, and the four- and six-probe configurations were used for electrical resistivity and Hall resistivity, respectively. The magnetoresistivity was symmetrized using ρxx(B) = (ρxx(B) + ρxx(−B))/2, and the Hall resistivity was antisymmetrized using ρxy(B) = (ρxy(B)−ρxy(−B))/2. The magnetization was measured using the QD Magnetic Properties Measurement System. The piece used for the magnetization measurement was later ground into fine powder, whose powder XRD pattern showed no impurity and was used for structural determination.

Single-crystal neutron diffraction

Single-crystal neutron diffraction experiments were performed at the HB-3A DEMAND single-crystal neutron diffractometer equipped with a 2D scintillation Anger camera with 0.6-mm spatial resolution at the High Flux Isotope Reactor at Oak Ridge National Laboratory in the temperature range of 4.5 to 15 K (54). Neutron wavelength of 1.551 Å was selected by using a bent perfect Si-220 monochromator. Rocking curve scans, which cover the full peak profile of the Bragg reflection (1 0 1), were carried out at 4.5 and 15 K, respectively. The peak (1 0 1) was selected for revealing the magnetic ordering parameter from 4.5 to 15 K.

First-principles calculations

The bulk band structures of MnBi8Te13 were computed using the projector augmented wave method as implemented in the VASP package (5557) within the GGA (58) and GGA plus Hubbard U (GGA + U) (59) scheme. On-site U = 5.0 eV was used for Mn d orbitals. The spin-orbit coupling was included self-consistently in the calculations of electronic structures with a Monkhorst-Pack k-point mesh 5 × 5 × 5. The experimental lattice parameters were used. The atomic positions were relaxed until the residual forces were less than 0.01 eV/Å. We used Mn d orbitals, Bi p orbitals, and Te p orbitals to construct Wannier functions, without performing the procedure for maximizing localization (60).

The surface spectral weight throughout the (001) surface BZ was calculated using the semi-infinite Green’s function approach for four distinct surface terminations. We set up four different models to calculate the surface state to compare with the ARPES data, for example, for the SL termination, the semi-infinite Green’s function model was set as vacuum-[SL-QL-QL-QL]-[SL-QL-QL-QL]-infinite; to get that of the QL1 termination, the model was set to be vacuum-[QL-SL-QL-QL]-[QL-SL-QL-QL]-infinite. This method was valid because the thickness of the QL or SL is about 10 Å, which roughly equals the typical escape depth of photoelectrons.

ARPES measurements

ARPES measurements on single crystals of MnBi8Te13 were carried out at the Stanford Synchrotron Research Laboratory (SSRL) beamline 5-2 with photon energies of 26 eV with linear horizontal polarization and a 20 μm× 50 μm beam spot. Single-crystal samples were top-posted on the (001) surface and cleaved in situ in an ultrahigh vacuum better than 4×10−11 torr and a temperature of 15 K.

SUPPLEMENTARY MATERIALS

Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/30/eaba4275/DC1

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REFERENCES AND NOTES

Acknowledgments: Funding: Work at UCLA was supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0011978. Work at CU Boulder was supported by NSF-DMR 1534734. Work at ORNL was supported by the U.S. DOE BES Early Career Award KC0402010 under contract DEAC05-00OR22725. This research used resources at the High Flux Isotope Reactor, DOE Office of Science User Facilities operated by the ORNL. We acknowledge M. Hashimoto and D.-H. Lu for help with the ARPES measurements. Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under contract no. DE-AC02-76SF00515. B.G. wants to acknowledge CSIR for the senior research fellowship. B.G. and A.A. thank CC-IITK for providing the HPC facility. T.-R.C. was supported by the Young Scholar Fellowship Program from the Ministry of Science and Technology (MOST) in Taiwan, under a MOST grant for the Columbus Program MOST108-2636-M-006-002, National Cheng Kung University, Taiwan, and National Center for Theoretical Sciences, Taiwan. This work was supported partially by the MOST, Taiwan, under grant MOST107-2627-E-006-001. This research was supported, in part, by Higher Education Sprout Project, Ministry of Education to the Headquarters of University Advancement at National Cheng Kung University (NCKU). TEM characterization and analysis were supported by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences (BES), Division of Materials Science and Engineering (DMSE) through Early Career Research Program under award KC0203020:67037. The work at Northeastern University was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences under grant no. DE-SC0019275, and benefited from Northeastern University’s Advanced Scientific Computation Center and the National Energy Research Scientific Computing Center through DOE grant no. DE-AC02-05CH11231. Author contributions: N.N. conceived the idea and organized the research. C.H., N.N., S.M., and J.L. grew the bulk single crystals and carried out x-ray, thermodynamic, and transport measurements and data analysis. H.C. and L.D. carried out structure determination and neutron diffraction measurements. K.N.G., H.Li, A.G.L., and D.D. carried out the ARPES measurements and data analysis. B.G., S.-W.L., H.-J.T., C.-Y.H., P.V.S.R., B.S., A.A., A.B., T.-R.C., S.-Y.X., and H.L. performed the first-principles calculations. M.S. and D.L. performed TEM measurements. All authors wrote the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
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